Spectral Extremal Results For Hypergraphs,
2021
University of South Carolina
Spectral Extremal Results For Hypergraphs, Yuan Hou, An Chang, Joshua Cooper
Faculty Publications
Let F be a graph. A hypergraph is called Berge F if it can be obtained by replacing each edge in F by a hyperedge containing it. Given a family of graphs F, we say that a hypergraph H is Berge F-free if for every F ∈ F, the hypergraph H does not contain a Berge F as a subhypergraph. In this paper we investigate on the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turán-type problems over linear k-uniform hypergraphs by using spectral methods.
Classification Of Holomorphic Functions As Pólya Vector Fields Via Differential Geometry,
2021
Illinois State University
Classification Of Holomorphic Functions As Pólya Vector Fields Via Differential Geometry, Lucian-Miti Ionescu, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae
Faculty Publications – Mathematics
We review Pólya vector fields associated to holomorphic functions as an important pedagogical tool for making the complex integral understandable to the students, briefly mentioning its use in other dimensions. Techniques of differential geometry are then used to refine the study of holomorphic functions from a metric (Riemannian), affine differential or differential viewpoint. We prove that the only nontrivial holomorphic functions, whose Pólya vector field is torse-forming in the cannonical geometry of the plane, are the special Möbius transformations of the form f(z)=b(z+d)−1" role="presentation">𝑓(𝑧)=𝑏(𝑧+𝑑)−1. We define and characterize several types of affine connections, related to the parallelism of Pólya …
A New Generalized Modified Weibull Distribution,
2021
Persian Gulf University-Bushehr
A New Generalized Modified Weibull Distribution, Morad Alizadeh, Muhammad Nauman Khan, Mahdi Rasekhi, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer’s G–function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as …
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions,
2021
Marquette University
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom
Mathematical and Statistical Science Faculty Research and Publications
This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fraction-related NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their …
Question Answering By Bert,
2021
Minnesota State University Moorhead
Question Answering By Bert, Suman Karanjit
Student Academic Conference
No abstract provided.
Analyzing Piney Point’S Wastewater Discharge Rate,
2021
University of South Florida
Analyzing Piney Point’S Wastewater Discharge Rate, Josephina Reyman
Undergraduate Journal of Mathematical Modeling: One + Two
Implicit differentiation is used in order to find the cubic feet of water dumped into Tampa Bay per hour from the Piney Point reservoir. To get to moles from cubic feet, a series of conversions is done while Le Chatelier’s principle explains how an increase in HPO4 2- (hydrogen phosphate) in Tampa Bay is going to affect algae growth. The rate of moles of HPO4 2- is analyzed as well as the consequences that come with dumping copious amounts of fertilizer water into an aquatic environment.
Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua,
2021
Université Libre de Bruxelles
Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Publications and Research
We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.
Special Types Of Tolerance And Control Solutions To System Of Interval Linear Equations,
2021
Faculty of Science
Special Types Of Tolerance And Control Solutions To System Of Interval Linear Equations, Warintorn Pongsumrankul
Chulalongkorn University Theses and Dissertations (Chula ETD)
In this thesis, we study a system of interval linear equations of the form Ax=b which includes an interval coefficient matrix and an interval right hand side vector. There are many types of solutions of this system which serve the different semantics in real-life situations such as tolerance and control solutions. We pay attention to the semantics that some boundaries of intervals are important. Moreover, we combine these semantics together with the semantics of tolerance and control solutions in order to present the new types of solutions to Ax=b, called special tolerance left, special tolerance right, special control left and …
Topics On Applications Of Optimization Theories On Statistical Methodologies,
2021
University of Mississippi
Topics On Applications Of Optimization Theories On Statistical Methodologies, Duc Anh Anh Doan
Electronic Theses and Dissertations
In this dissertation, We show the results of our researches in statistical sampling, functional optimization, and methodology for partially observed Markov process (POMP) models. In statistical sampling, we introduce a p-generalized smoothing method that enables the Langevin-Monte Carlo method to generate a sample from a log concave distribution weakly smoothing potential function. For our optimization research, we introduce an accelerated inexact gradient (AIG) method. Combining the strengths while mitigating the weakness of its parent methods: gradient descent and Nesterov's accelerated gradient, AIG converges with excellent rates for both convex and non-convex optimization problems for smooth objective functions. Furthermore, we also …
Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals,
2021
Old Dominion University
Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals, Wesley Davis, Richard D. Noren
Mathematics & Statistics Faculty Publications
We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order integrals using Taylor and fractional Taylor series expansions and grouping terms in a novel manner. A fractional Taylor series expansion argument is utilized to provide fractional-order approximations for functions with minimal regularity. The resulting schemes allow for the approximation of functions in Cγ [0, T], where 0 < γ <= 5. A mild invertibility criterion is provided for the implicit schemes. Consistency and stability are proven separately for the whole-number-order approximations and the fractional-order approximations. The rate of convergence in the time variable is shown …
Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula,
2021
Old Dominion University
Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula, Hasika K. W. Senevirathne, Ananda B.W. Manage
Mathematics & Statistics Faculty Publications
The Pythagorean Win-Loss formula can be effectively used to estimate winning percentages for sporting events. This formula was initially developed by baseball statistician Bill James and later was extended by other researchers to sports such as football, basketball, and ice hockey. Although one can calculate actual winning percentages based on the outcomes of played games, that approach does not take into account the margin of victory. The key benefit of the Pythagorean formula is its utilization of actual average runs scored and actual average runs allowed. This article presents the application of the Pythagorean Win-Loss formula to two different types …
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders,
2021
Pitzer College
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Pitzer Senior Theses
This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …
Optimal Tile-Based Dna Self-Assembly Designs For Lattice Graphs And Platonic Solids,
2021
Stonehill College
Optimal Tile-Based Dna Self-Assembly Designs For Lattice Graphs And Platonic Solids, Leyda Almodovar, Joanna Ellis-Monaghan, Amanda Harsy, Cory Johnson, Jessica Sorrells
Mathematics Faculty Publications
A design goal in self-assembly of DNA nanostructures is to find minimal sets of branched junction molecules that will self-assemble into targeted structures. This process can be modeled using techniques from graph theory. This paper is a collection of proofs for a set of DNA complexes which can be represented by specific graphs, namely Platonic solids, square lattice graphs, and triangular lattice graphs. This work supplements the results presented in https://arxiv.org/abs/2108.00035
Analytical And Numerical Monotonicity Results For Discrete Fractional Sequential Differences With Negative Lower Bound,
2021
University of Nebraska at Omaha
Analytical And Numerical Monotonicity Results For Discrete Fractional Sequential Differences With Negative Lower Bound, Christopher S. Goodrich, Benjamin Lyons, Mihaela T. Velcsov
Mathematics Faculty Publications
We investigate the relationship between the sign of the discrete fractional sequential difference(Δv1+a-μ Δaμf)(t) and the monotonicity of the function t→f(t). More precisely, we consider the special case in which this fractional difference can be negative and satisfies the lower bound (Δv1+a-μ Δaμf)(t) ≥ -εf(a), for some ε >0. We prove that even though the fractional difference can be negative, the monotonicity of the function f, nonetheless, is still implied by the above inequality. This demonstrates a significant dissimilarity between the fractional and non-fractional cases. Because of the challenges …
The Plus-Minus Davenport Constant Of Finite Abelian Groups,
2021
University of Kentucky
The Plus-Minus Davenport Constant Of Finite Abelian Groups, Darleen S. Perez-Lavin
Theses and Dissertations--Mathematics
Let G be a finite abelian group, written additively. The Davenport constant, D(G), is the smallest positive number s such that any subset of the group G, with cardinality at least s, contains a non-trivial zero-subsum. We focus on a variation of the Davenport constant where we allow addition and subtraction in the non-trivial zero-subsum. This constant is called the plus-minus Davenport constant, D±(G). In the early 2000’s, Marchan, Ordaz, and Schmid proved that if the cardinality of G is less than or equal to 100, then the D±(G) …
The Smallest Solution Of An Isotropic Quadratic Form,
2021
University of Kentucky
The Smallest Solution Of An Isotropic Quadratic Form, Deborah H. Blevins
Theses and Dissertations--Mathematics
An isotropic quadratic form f(x1,...,xn) = ∑ ni=1 ∑ nj=1 fijxixj defined on a Z- lattice has a smallest solution, where the size of the solution is measured using the infinity norm (∥ ∥∞), the l1 norm (∥ ∥1), or the Euclidean norm (∥ ∥2). Much work has been done to find the least upper bound and greatest lower bound on the smallest solution, beginning with Cassels in the mid-1950’s. Defining F := (f11,...,f …
Maximums Of Total Betti Numbers In Hilbert Families,
2021
University of Kentucky
Maximums Of Total Betti Numbers In Hilbert Families, Jay White
Theses and Dissertations--Mathematics
Fix a family of ideals in a polynomial ring and consider the problem of finding a single ideal in the family that has Betti numbers that are greater than or equal to the Betti numbers of every ideal in the family. Or decide if this special ideal even exists. Bigatti, Hulett, and Pardue showed that if we take the ideals with a fixed Hilbert function, there is such an ideal: the lexsegment ideal. Caviglia and Murai proved that if we take the saturated ideals with a fixed Hilbert polynomial, there is also such an ideal. We present a generalization of …
A Tropical Approach To The Brill-Noether Theory Over Hurwitz Spaces,
2021
University of Kentucky
A Tropical Approach To The Brill-Noether Theory Over Hurwitz Spaces, Kaelin Cook-Powell
Theses and Dissertations--Mathematics
The geometry of a curve can be analyzed in many ways. One way of doing this is to study the set of all divisors on a curve of prescribed rank and degree, known as a Brill-Noether variety. A sequence of results, starting in the 1980s, answered several fundamental questions about these varieties for general curves. However, many of these questions are still unanswered if we restrict to special families of curves. This dissertation has three main goals. First, we examine Brill-Noether varieties for these special families and provide combinatorial descriptions of their irreducible components. Second, we provide a natural generalization …
Weight Distributions, Automorphisms, And Isometries Of Cyclic Orbit Codes,
2021
University of Kentucky
Weight Distributions, Automorphisms, And Isometries Of Cyclic Orbit Codes, Hunter Lehmann
Theses and Dissertations--Mathematics
Cyclic orbit codes are subspace codes generated by the action of the Singer subgroup Fqn* on an Fq-subspace U of Fqn. The weight distribution of a code is the vector whose ith entry is the number of codewords with distance i to a fixed reference space in the code. My dissertation investigates the structure of the weight distribution for cyclic orbit codes. We show that for full-length orbit codes with maximal possible distance the weight distribution depends only on q,n and the dimension of U. For full-length orbit codes with …
Solubility Of Additive Forms Over Local Fields,
2021
University of Kentucky
Solubility Of Additive Forms Over Local Fields, Drew Duncan
Theses and Dissertations--Mathematics
Michael Knapp, in a previous work, conjectured that every additive sextic form over $\mathbb{Q}_2(\sqrt{-1})$ and $\mathbb{Q}_2(\sqrt{-5})$ in seven variables has a nontrivial zero. In this dissertation, I show that this conjecture is true, establishing that $$\Gamma^*(6, \mathbb{Q}_2(\sqrt{-1})) = \Gamma^*(6, \mathbb{Q}_2(\sqrt{-5})) = 7.$$ I then determine the minimal number of variables $\Gamma^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=2m$, $m$ odd, $m \ge 3$ over the six ramified quadratic extensions of $\mathbb{Q}_2$. We prove that if $$K \in \{\mathbb{Q}_2(\sqrt{2}), \mathbb{Q}_2(\sqrt{10}), \mathbb{Q}_2(\sqrt{-2}), \mathbb{Q}_2(\sqrt{-10})\},$$ then $$\Gamma^*(d,K) = \frac{3}{2}d,$$ and if $$K \in \{\mathbb{Q}_2(\sqrt{-1}), \mathbb{Q}_2(\sqrt{-5})\},$$ then $$\Gamma^*(d,K) = …
